Physics Relativistic Motion

Objectives By the end of this lesson, you should be able to Explain the General Theory of Relativity as it relates to velocity Calculate the dilation factor based on an objects relativistic speed Apply the dilation factor to time dilation Apply the dilation factor to length contraction

Standards SP6. The student will describe the corrections to Newtonian physics given by quantum mechanics and relativity when matter is very small, moving fast compared to the speed of light, or very large.

Catch me if you can Up until now, all of the speeds we have dealt with have primarily been somewhat slow in the grand scheme of things Through various scientific tests, we have determined that light is the fastest thing in the universe Instead of writing v or v light or even v l, we just use the letter c c = 3x10 8 m/s This is the speed of light in a vacuum (as in space, not as in a Hoover) NOTE: There is a hypothetical particle known as a tachyon that supposedly travels faster than light; it has not been proven to exist

General Relativity Albert Einstein is known for several major impacts to scientific thought One of them is general relativity Among other things, general relativity relates high speed, distances, and time An idea within general activity is that time moves at different rates depending on the speed of the observer and observee

Thought experiment Imagine a person bouncing a ball on a moving train straight up and down The motion that is observed inside the train is Now imagine that a person is standing outside the train and is able to observe the ball moving as the train passes by The motion that is observed outside the train is

The person inside the train observes the ball moving a much shorter distance with one bounce than the person outside the train does Who is correct? They both are! Image thanks to: win_corduan.tripod.com%2Fphysics.html&psig=AFQjCNHptx637upo9 Aqd-wsM5yGq3T_wNg&ust=

The more things change Remember that velocity has a formula: v = Δx/t If the ball was actually a ball of light, then v is the speed of light c = Δx/t If distance changes and the speed of light is a constant, then that must mean that time is different for the person inside and the person outside

Dilation factor There is a way to calculate the difference To do it, you will need the formula to determine the dilation factor Dilation factor: 1 – v 2 /c 2 Where v is the speed that you are travelling and c is the speed of light So, if you where travelling at ½ the speed of light 1 – (.5c) 2 /c 2 = 1 –.25 =.75 =.866

Application of dilation In the previous example, you are travelling at ½ the speed of light In that example, the dilation factor was.866 This means that time is literally moving 86.6% as fast for you as compared to an observer One hour of the observer’s time would only be (.866x60min) about 52 minutes of your time One hour of your time would be (60 /.866) about one hour and 9 minutes of the observers This doesn’t mean that you think that time is moving slower (as in “it feels like time is dragging by”) – time itself is actually moving slower

Not just a theory Einstein was a great theoretical scientists This means that he didn’t prove any of his own theories The theory of relativity needed experimental scientists to conduct experiments to support the theory One example of a test Two atomic clocks were perfectly synchronized One was placed onto a high speed aircraft and the other was left on the ground After the aircraft flew a distance, the clocks were reexamined The clock on the ground showed a later time than that from the plane

Twins! A classic thought experiment is the following Two identical twins are chosen for an experiment One twin will be depart the Earth, travel in a spacecraft near the speed of light, and then return The other twin would remain on the Earth When the travelling twin returned, he or she would be younger than the twin that was left behind

Twins How fast was the ship travelling? Example A: If it travelled 90% of the speed of light, or.9c, the dilation would be.435 If 10 years passed for the twin on Earth, only 4.35 years would have passed for the travelling twin Example B: If it travelled 99% of the speed of light, or.99c, the dilation would be.141 If 10 years passed for the twin on Earth, only 1.41 years would have passed for the travelling twin

Possibly easier to understand… Spoiler alert: another part of general relativity will be revealed

Ramifications One impact of this theory was that it shattered the idea of absolute time NOTE: Technically, if you are an active person, you actually do have more time in your day compared to another person (albeit an extremely small amount of time) Another realization is that if a person could ever actually reach the speed of light, time would stand still for that person

The journey of a thousand miles… We’ll pretend that you have to go between two locations Your ship will travel ½ the speed of light (.5c) Your ship will travel two a star 4 light years away as measured on Earth An observer on Earth would see it take you 8 years to reach your location Due to dilation, your clocks will only show (8*.866) approximately 6.9 years

A bad case of foreshortening In the previous example Your 4 light year journey was took 8 years, as measured on Earth It took 6.9 years as measured on your ship Both you and the observer know that you are travelling at.5c This means, that distances are relative also! On your ship, you have travelled 3.45 light years….to the same location Length contraction is the change of length/distance as speed increases